Re: Category Theory of Algorithms

On Apr 10, 12:32 am, "the.theorist" <the.theor...@xxxxxxxxx> wrote:

In which area?

The area of studying algorithms as mathematical objects, with closure
under some set of operations.

We're not sure to answer probably because of cultural baggage that
goes with the terms you are using.

'Algorithms' (or anything with algorithm in it) usually refers to the
study of design and analysis of specific problems: e.g. shortest
paths, string matching, matrix multiplication, satisfiability of
logical formulas. Take a particular problem, solve it.

With that in mind, there really isn't much idea of studying operations
on those algorithms; one might study a set of operations that are used
-in- an algorithm, but not operations between algorithms (er... except
maybe reduction).

The closest I can imagine to what you are looking for is really in -
programming language theory-, where you -do- compose separate pieces
of (arbitrary) code with different operations, and there is a well
studied (and continuing study) application of category theory to
programming languages. The text that is most familiar to me is

Carl Gunter, Semantics of Programming Languages: Structures and
Techniques (Foundations of Computing)

the key word to look for for other texts/references is programming
language semantics.

See what I'm after is an algebra of algorithms. I'd like to know if
it's possible to take some small set of simple algorithms, and by
repeated application of some operators build up to more complex
algorithms. An, Algebra or Calculus of Algorithms, if you will.

Now, since nobody has applied Category Theory to the study of
algorithms in the manner I was talking about, perhaps there have been
difficulties, and it's been to hard. If that's the case, then: What,
specifically, are those difficulties?

1) if you really meant what other people mean by programming language
semantics then many people have worked on it.

2) if you really do mean -algorithms-... my imagination is too small
to think of anything other than this line of thought leading back
towards programming language semantics. Maybe if you give a more
specific example of what you're looking for.

Mitch

.

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